Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.     

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

The Rayleigh–Taylor instability(RTI) in cylindrical geometry is investigated analytically through a second-order weakly nonlinear(WN) theory considering the Bell–Plesset(BP) effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.     

Cylindrical effects in weakly nonlinear Rayleigh Taylor instability

The classical Rayleigh–Taylor instability(RTI)at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order.Two styles of RTI,convergent(i.e.,gravity pointing inward)and divergent(i.e.,gravity pointing outwards)configurations,compared with RTI in Cartesian geometry,are taken into account.Our explicit results show that the interface function in the cylindrical geometry consists of two parts:oscillatory part similar to the result of the Cartesian geometry,and non-oscillatory one contributing nothing to the result of the Cartesian geometry.The velocity resulting only from the non-oscillatory term is followed with interest in this paper.It is found that both the convergent and the divergent configurations have the same zeroth-order velocity,whose magnitude increases with the Atwood number,while decreases with the initial radius of the interface or mode number.The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

On the Second Harmonic Generation through Bell-Plesset Effects in Cylindrical Geometry

Generation of the second harmonic initiated by Bell-Plesset effects in a cylindrical geometry is studied analytically. For an initial single-mode velocity perturSation, the second-order mode-coupling formula is obtained by expanding the perturbation displacement and velocity potential up to the second-order accuracy. It is found that the initially symmetric interface evolves into a significant bubble-spike asymmetric pattern. The second-order solutions clearly show that the amplitude of the spike grows faster than that of the buSble. The temporal evolutions of the amplitudes of the 5ubSie and spike are dependent on the interface velocity Vo. The larger interface velocity leads to the smaller amplitude of the perturbation at an arbitrary interface position in a cylindrically convergent geometry.     

RT instability in cylindrical implosion of jelly ring

The interfacial RT instability experiments on imploding jelly liners in cylindrically convergent geometry have been performed. The liner‘s instability growth was observed clearly with a high-speed framing camera. Jelly liners have different initial perturbation forms on their inner and outer interfaces, being either smooth or sinusoidal. The initial perturbations also have different magnitudes and spatial frequencies (for example, mode n=-5, 10, 20). The experimental results show that the growth and coupling of perturbations on inner and outer surfaces are remarkably different. Meanwhile, the relevant 2-D numerical simulation of hydrodynamics combined with Level Set method has been performed. Using the numerical code, we can design the parameters of imploding jelly liner, and predict the experimental results. The results of simulation are demonstrated to be in good agreement with the measured data in a series of experiments.     

Electron-Phonon Interaction in an Annular Quantum Dot

The confined longitudinal-optical （LO） phonon and surface-optical （SO） phonon modes of a free-standing annular cylindrical quantum dot are derived within the framework of dielectric continuum approximation. It is found that there exist two types of SO phonon modes： top SO （TSO） mode and side SO（SSO） mode in a cylindrical quantum annulus. Numerical calculation on CdS annulus system has been performed. Results reveal that the two different solutions of SSO mode distribute mainly at the inner or outer surfaces of the annulus. The dispersion relations and the coupling intensions of phonons in a quantum annulus are compared with those in a cylindrical quantum dot. It is found that the dispersion relations of the two different structures are similar, but the coupling intension of the phonon-electron interaction in quantum annulus is larger than that in quantum dot. The Hamiltonians describing the free phonon modes and their interactions with electrons in the system are also derived.     

Linear stability analysis on a spherical particle growing from a binary melt under the far-field flow

The solutions of temperature and solute fields around a spherical crystal growing from a binary melt under the far-field flow are obtained.Based on the results,a linear stability analysis on the spherical interface growing from the binary melt under the far-field flow is performed.It is found that the constitutional supercooling effect ahead of the spherical crystal interface under the far-field flow is enhanced compared with that without the flow.The growth rate of the perturbation amplitude at the up-wind side of the spherical crystal interface is larger than that at the down-wind side.The critical stability radius of the crystal interface decreases with the increasing far-field flow velocity.Under the far-field flow,the whole spherical interface becomes more unstable compared with that without the flow.     

Interface coupling effects of weakly nonlinear Rayleigh–Taylor instability with double interfaces

Taking the Rayleigh–Taylor instability with double interfaces as the research object,the interface coupling effects in the weakly nonlinear regime are studied numerically.The variation of Atwood numbers on the two interfaces and the variation of the thickness between them are taken into consideration.It is shown that,when the Atwood number on the lower interface is small,the amplitude of perturbation growth on the lower interface is positively related with the Atwood number on the upper interface.However,it is negatively related when the Atwood number on the lower interface is large.The above phenomenon is quantitatively studied using an analytical formula and the underlying physical mechanism is presented.     

Influence of isothermal approximation on the phase-field simulation of directional growth in undercooled melt

By using the phase-field approach,we have simulated the directional growth of alloys in undercooled moten states under the isothermal and nonisothermal conditions.The influences of the isothermal approximation on simulation results are discussed.We found that for undercooling greater than 25K,the isothermal approximation overestimates the interface growth velocity and reduces a critical velocity for an absolute stable planar interface,thus in this simulation,the uinterface morphology shows the plane-cell-plane transition with increasing initial undercooling of the mele,and the planar interface obtained under a large undercooling is absolutely stable.Whereas in the nonisothermal simulation,only plane-cell transition occures in the same range of the initial undercoolings of the melt,and the planar interface tends to be destabilized and evolve into cells.     

Evanescent waves of an annular left-handed material lens

The imaging system formed by an annular left-handed material （LHM） lens as well as the evanescent waves in the lens are simulated numerically with a finite-difference time-domain （FDTD） method. For b - a 〉 λ （a and b are respectively the inner and outer radii of the annular lens, and λ is the wavelength）, when a point source is placed at an internal grid point, we demonstrate that the evanescent waves are produced around the internal interface, and cannot propagate outwards. As for b - a 〈λ ）,, the evanescent waves appear around both the internal and the external interfaces, which remarkably implies the coupling between the two interfaces. Hence it can be inferred that the evanescent waves around the external interface participating in the super-resolution imaging result from the coupling of the evanescent waves around the interface. Moreover, the partly uncomprehended properties of the evanescent waves in the LHM slab are also disclosed. It is conducive to understanding the evanescent waves in the LHMs further.     

Nucleus-acoustic solitary waves in self-gravitating degenerate quantum plasmas

Nucleus-acoustic(NA) solitary waves(SWs) propagating in a self-gravitating degenerate quantum plasma(SDQP)system(containing non-relativistically degenerate heavy and light nuclei,and non-/ultra-relativistically degenerate electrons) have been theoretically investigated.The modified Korteweg–de Vries(m K-d V) equation has been derived for both planar and non-planar geometry by employing the reductive perturbation technique.It is shown that the NA SWs exist with positive(negative) electrostatic(self-gravitational) potential.It is also observed that the effects of non-/ultra-relativistically degenerate electron pressure,dynamics of non-relativistically light nuclei,spherical geometry,etc.significantly modify the basic features(e.g.,amplitude,width,speed,etc.) of the NA SWs.The applications of our results,which are relevant to astrophysical compact objects,like white dwarfs and neutron stars,are briefly discussed.     

Kinetics of Spherical Interface in Crystal Growth

The growth kinetics of spherical NiAl and CuZr crystals are studied by using molecular dynamics simulations.The growth rates of crystals are found to increase with the grain radius. The simulations show that the interface thickness and the Jackson α-factor increase as the growth proceeds, indicating that the interface becomes increasingly rough during growth. Due to the increasing interface roughening, the fraction of repeatable growth sites at interface f is proposed to actually increase in growth. An attachment rate, which is defined as the fraction of atoms that join the crystal interface without leaving, is used to approximate f, displaying a linear increase. With this approximation, we predict the growth rates as a function of the crystal radius, and the results qualitatively agree with those from the direct simulations.     

Atomic and Electronic Structures of Zr Atomic Chains

The atomic, binding and electronic structures of very thin Zr chains are studied by the first-principles density functional method. The present calculations reveal that zirconium can form planar chains in zigzag, dimer and ladder structures. The zigzag geometry has two minima. The most stable geometry is the zigzag one with a unitcell rather close to equilateral triangles with four nearest neighbours. The other stable zigzag structure has awide bond angle and allows for two nearest neighbours. An intermediary structure has the ladder geometry andis formed by two strands. The dimer structure is also found to be more stable than the truly linear chain. Allthese planar geometries are more favourable energetically than the linear chain. We also show that by going fromZr bulk to a Zr chain, the characters of bonding do not change significantly.     

Interface Properties of InAs／AlSb Superlattices Characterized by Grazing Incidence X-Ray Reflectivity

Two kinds of superlattice interfaces of InAs/AlSb superlattices are realized in an optimized interface growth process, where one is AlAs-like and the other is InSb-like grown on a relaxed AlSb buffer layer. The superlattice properties such as interface roughness and layer thickness are studied by grazing incidence x-ray reflectivity. The reflectivity curves are simulated by standard software till the simulation curves match well with the experimental curves. The simulation indicates that AlAs-like interfaces are much rougher than InSb-like interfaces. Grazing incidence x-ray reflectivity is also discussed as a powerful tool to assessing the structure properties of superlattices.     

Head-on collision of ring dark solitons in Bose--Einstein condensates

The ring dark solitons and their head-on collisions in a Bose--Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincar\'e--Lighthill--Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate $r$ according to the $r^{-1/3}$ law and depend on the initial soliton amplitude and radius.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

Vibration coupling effects between two concentric cylindrical shells through periodic annular plates and entrained fluid

The coupling effects on two concentric cylindrical shells with periodic annular plates as well as entrained fluid were investigated theoretically. Expressions for the reactive forces by the annular plates were derived on the assumption that only quasi-longitudinal waves exist in the annular plates and an analytical expression for the outer shell was developed. Comparisons of numerical results for infinite two-walled cylindrical shell to measured data for a cabin model are in good agreement. Numerical results were presented for analyzing the characteristics of the loadings due to the acoustic fluid and the periodic annular plates, and their influences on the outer shell＇s far field acoustic radiation.     

Interface Width Effect on the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

Interface width effect on the spherical Rayleigh–Taylor instability in the weakly nonlinear regime is studied by numerical simulations.For Legendre perturbation mode P_n with wave number K_n and interface half-width L,the commonly adopted empirical linear growth rate formula γ_n~(em)(L)=γn/√1 + K_nL is found to be sufficient in spherical geometry.At the weakly nonlinear stage,the interface width affects the mode coupling processes.The development of the mode P_(2n) is substantially influenced by the interface width.Moreover,the nonlinear saturation amplitude increases with the interface width.     

Molecular dynamics simulation of cylindrical Richtmyer-Meshkov instability

The microscopic-scale Richtmyer-Meshkov(RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude,wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio(η). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to η, while the second one depends heavily on it.